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POST UTME ABU 2020 Mathematics | Objective

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Question 1 View Details

A cylindrical \tank with a radius of 7m and a height of 10m is filled with water. What is the volume of water in the \tank, in cubic meters?

Correct A. 700\pi

B. 700\pi + 100\pi

C. 700\pi - 100\pi

D. 100\pi

Correct Answer: A

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Question 2 View Details

A histogram is constructed from the following data: 2, 4, 5, 6, 8, 9, 11, 12, 14, 16. What is the mean of the data set?

Correct A. 7.5

B. 8.5

C. 9.5

D. 10.5

Correct Answer: A

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Question 3 View Details

Solve the equation: \log_{10} \(x^2 = 4\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 4 View Details

A quadratic equation is given by: \\((x^2 + 5x + 6\)\(= 0.\)\) Find the roots of the equation.

Correct A. \(x = -2\),\(x = -3\)

B. \(x = -1\),\(x = -6\)

C. \(x = 2\), \(x = 3\)

D. \(x = -1\), \(x = 6\)

Correct Answer: A

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Question 5 View Details

A rectangular prism has a length of 5m, a width of 3m, and a height of 2m. What is the surface area of the prism?

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 6 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(\frac{1}{2}\\()x^2 - 2x + 3\)\), the \\((y = frac{1}{2}x^2 - 2x + 3\(x)-axis, and the line \(x = 1\) about the \\()-axis, and the line (x = 1\(x\)-axis.

Correct A. \(\frac{\pi}{6}\)\)

B. \(\frac{\pi}{3}\)\)

C. \(\frac{\pi}{2}\)\)

D. \(\frac{\pi}{4}\)\)

Correct Answer: A

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Question 7 View Details

Solve the inequality \(\log_{10} x^2 - 4\)\(> 2\)\).

A. \(x > 4\)

B. \(x < -4\)

Correct C. \(x > 2\) or x < -2

D. \(x > 2\) or \(x < 2\)

Correct Answer: C

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Question 8 View Details

Find the equation of the circle passing through the points \((1, 2)\) and \(-2, 3\)\).

Correct A. \(x^2\) + \\((y^2 - 4x - 6y + 13\)\(= 0\)\)

B. \(x^2\) + \\((y^2 + 4x + 6y + 13\)\(= 0\)\)

C. \(x^2\) + \\((y^2 - 4x + 6y + 13\)\(= 0\)\)

D. \(x^2\) + \\((y^2 + 4x - 6y + 13\)\(= 0\)\)

Correct Answer: A

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Question 9 View Details

Solve the system of equations \(\begin{cases} x + y = 2 \ x - 2y = -3 \end{cases}\).

Correct A. \(x = 1\), \(y = 1\)

B. \(x = -1\), \(y = 3\)

C. \(x = 1\), \(y = 3\)

D. \(x = -1\), \(y = 1\)

Correct Answer: A

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Question 10 View Details

Find the area of the triangle with vertices \((0, 0)\), \((3, 0)\), and \((0, 2)\).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 11 View Details

A binary number is represented as \(1010_2\). What is the decimal equivalent of this number?

A. 10

Correct B. 11

C. 12

D. 13

Correct Answer: B

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Question 12 View Details

A random experiment has two possible outcomes: A and B. The probability of outcome A is ( P(A) = \(\frac{1}{3}\)\) ). What is the probability of outcome B?

A. \(1/3\)

Correct B. \(2/3\)

C. \(1/2\)

D. \(4/5\)

Correct Answer: B

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Question 13 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\) using integration.

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 14 View Details

A set of exam scores has a mean of 80 and a standard deviation of 5. What is the z-score of a score of 90?

A. 0.8

B. 1.2

Correct C. 1.6

D. 2.0

Correct Answer: C

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Question 15 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 2 cm. What is its volume?

Correct A. 48

B. 64

C. 80

D. 96

Correct Answer: A

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Question 16 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pi \(cm^3\)

Correct B. 48\pi \(cm^3\)

C. 96\pi \(cm^3\)

D. 192\pi \(cm^3\)

Correct Answer: B

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Question 17 View Details

If f(x) = \(3x^2 + 2x - 5\) and g(x) = \(2x^2 - 3x + 1\), find the derivative of f(g(x)) using the chain rule.

A. \(6x^3 - 12x^2 + 6x + 4\)

B. \(12x^3 - 18x^2 + 6x - 2\)

Correct C. \(24x^3 - 36x^2 + 12x - 6\)

D. \(48x^3 - 72x^2 + 24x - 12\)

Correct Answer: C

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Question 18 View Details

A die is rolled three times. What is the probability that the sum of the three rolls is 9?

Correct A. \(\frac{1}{8}\)\)

B. \(\frac{1}{6}\)\)

C. \(\frac{1}{4}\)\)

D. \(\frac{1}{2}\)\)

Correct Answer: A

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Question 19 View Details

Find the sum of the first 10 terms of the geometric series 2x + \(4x^2 + 8x^3\) + ...

A. \(2048x^{10}\)

B. \(4096x^{10}\)

Correct C. \(8192x^{10}\)

D. \(16384x^{10}\)

Correct Answer: C

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Question 20 View Details

Solve the quadratic equation \\((x^2 + 5x + 6\)\(= 0\)\) using the quadratic formula.

Correct A. x = -2 or x = -3

B. x = -1 or x = -6

C. \(x = 1\) or x = -6

D. \(x = 2\) or x = -3

Correct Answer: A

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Question 21 View Details

Find the area under the curve \(y = x\^2 + 2x - 3\) from \(x = 0\) to \(x = 3\).

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 22 View Details

Solve the equation \\((2x^2 + 5x - 3\)\(= 0\)\) using the quadratic formula.

Correct A. \(1/2\)

B. \(-1/2\)

C. 1

D. -1

Correct Answer: A

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Question 23 View Details

Find the derivative of the function f(x) = \(x^3 - 2x^2 + x - 1\).

Correct A. \(3x^2 - 4x + 1\)

B. \(x^2 - 2x + 1\)

C. \(x^3 - 2x^2 + x - 1\)

D. \(x^2 + 2x - 1\)

Correct Answer: A

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Question 24 View Details

Solve the trigonometric equation \\(sin(x) =\)\cos(x).

Correct A. \(x =\)π/4

B. \(x =\)π/2

C. \(x = 3\)π/4

D. \(x =\)π

Correct Answer: A

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Question 25 View Details

Find the vector projection of the vector (b = 2i + 3j\) onto the vector \(a = i + 2j\\((b = 2i + 3j) onto the vector\).

Correct A. \(1/3\) i + \(2/3\) j

B. \(2/3\) i + \(1/3\) j

C. \(1/2\) i + \(1/2\) j

D. \(1/4\) i + \(3/4\) j

Correct Answer: A

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